Finslerian and higher-order structure of space-time: Lie-invariance in fibres
type: Item
instance of: scholarly article
title: Finslerian and higher-order structure of space-time: Lie-invariance in fibres
zbMATH Open document ID: 0733.53010
DOI: 10.1016/0034-4877(89)90048-7
published in: Reports on Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: In some recent papers [Rep. Math. Phys. 26, No.3, 367-399 (1988; Zbl 0691.53058)] the author proposed and investigated fibre-generalized gauge covariant field equations but did not include any Lie-invariance concepts. In this paper such an idea is taken into consideration assuming that each fibre has a Lie-group structure. The gauge fields are subject to conditions of Lie-invariance which ensure the Lie-invariance of the operator of covariant differentiation. Then by introducing the notion of a Lie-invariant field it is shown that all generalized gauge tensors are Lie-invariant. The homogeneous case is studied also. Assuming that all group structures in the fibres are isomorphic to each other, a kind of normal coordinates is introduced in order to simplify the calculations.
Mathematics Subject Classification ID: 53C07
Mathematics Subject Classification ID: 53C60
zbMATH DE Number: 4212915
zbMATH Keywords: fibre-generalized gauge covariant field equations
zbMATH Keywords: Lie-invariance
zbMATH Keywords: Lie- group structure
author: Gennadii S. Asanov
MaRDI profile type: Publication
full work available at URL: 0034-4877(89)90048-7
OpenAlex ID: W2056257173
cites work: Finsler geometry, relativity and gauge theories
cites work: Finslerian fibered extension of gauge field theory: Lie-invariance in fibres and effective Lagrangian
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cites work: On non-compact groups I. Classification of non-compact real simple Lie groups and groups containing the Lorentz group
cites work: Q3896182
description: scientific article; zbMATH DE number 4212915